Problem: Simplify the following expression: $k = \dfrac{-8p - 24}{4}$ You can assume $p \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-8p - 24 = - (2\cdot2\cdot2 \cdot p) - (2\cdot2\cdot2\cdot3)$ The denominator can be factored: $4 = (2\cdot2)$ The greatest common factor of all the terms is $4$ Factoring out $4$ gives us: $k = \dfrac{(4)(-2p - 6)}{(4)(1)}$ Dividing both the numerator and denominator by $4$ gives: $k = \dfrac{-2p - 6}{1}$ or more simply, $k = -2p - 6$